The short answer to your question is "Yes it will".
But the longer answer is "But not by very much because ..................".
To understand why this is the case you we need to look at the amount by which varying humidity will affect air density.
If we compare the densities of pure water vapour and dry air at the same temperature and pressure we will find that the density of water vapour is about 63% of that of dry air.
If we then look at how much water vapour can be held in air we find that at 20 degrees Celsius at sea level saturated air contains about 1.8% water vapour.
If we combine these two figures we will find that the difference in density between dry air and saturated air is very small.
So the increase in take-off distance is also very small.